Mathematical Visualization in Snow

2005: Knot Divided

I am part of "Team Minnesota",
led by Stan Wagon,
a mathematician at Macalester College
in Minnesota, who has entered the competition for 7 years in a row now,
doing a mathematical visualization in snow sculpture each year.
Stan has nice online reports about the team's
past work,
including a silver-medal winner in 2003. In 2004, we got an honorable
mention ("Most Ambitious Piece") for our entry
Turning a Snowball Inside Out,
a depiction of a sphere eversion.

Our entry this year, entitled
Knot Divided
starts out as a trefoil knot, tied with 3/2 twist in a tube of rectangular
cross-section. We then slit the rectangle down the middle, leaving
two U-shaped cross-sections. The original Möbius band has
been cut in half to form a single longer strand, now forming a
fifteen-crossing knot. The design again comes from
Carlo Séquin.

Please check back here, and at Stan
and Carlo's
webpages, for daily updates during the competition, 25 - 29 January.

My photos from our practice run the two days
before the competition are available
here;
see also highlights.
c/o Stan Wagon.

The second day, 26 January, we worked from 8am to 9pm.
We tried to get the main loops isolated, but there's more
of that to do tomorrow. See
highlights,
my complete photos,
and selected photos by Carlo and Rich.

The third day, 27 January, we worked long hours again,
finishing the definition of the rectangular cross-seciton, and starting
to split it apart into two lobes. See
highlights,
my complete photos,
and selected photos by Carlo.

The fourth day, 27 January, we completed the sculpture,
except for final finishing, without even having to stay up all night.
See my complete photos,
and selected photos by Carlo and Rich.

The final day, 28 January, we worked for almost 4 hours before
the 10am deadline. We were pleased with the final sculpture,
though it didn't win any prizes.
See my complete photos,
and selected photos by Rich.